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Section 13.7

Section 13.7. Cylindrical and Spherical Coordinates. THE CYLINDRICAL COORDINATE SYSTESM. In the cylindrical coordinate system , a point P in space is represented by the ordered triple ( r, θ , z ), where. 1. r and θ are polar coordinates of the projection of P onto the xy -plane;

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Section 13.7

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  1. Section 13.7 Cylindrical and Spherical Coordinates

  2. THE CYLINDRICAL COORDINATE SYSTESM In the cylindrical coordinate system, a point P in space is represented by the ordered triple (r,θ, z), where 1. r andθ are polar coordinates of the projection of P onto the xy-plane; 2. z is the directed distance from the xy-plane to P.

  3. CONVERTING BETWEEN CARTESIAN AND CYLINDRICAL COORDINATES Cylindrical to Cartesian Cartesian to Cylindrical

  4. THE SPHERICALCOORDINATE SYSTEM In the spherical coordinate system, the point P is represented by (ρ, θ,φ) where • ρ is the distance between P and the origin O, ρ ≥ 0; • θ is the same angle used in cylindrical coordinates for r ≥ 0; and • φ is the angle between the positive z-axis and the line segment OP. 0 ≤ φ ≤ π.

  5. CONVERTING BETWEEN CARTESIAN AND SPHERICAL COORDINATES Spherical to Cartesian Cartesian to Spherical

  6. CONVERTING BETWEEN CYLINDRICAL AND SPHERICAL COORDINATES Cylindrical to Spherical Spherical toCylindrical

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